Finsler metrics: a global approach ; with applications to geometric function theory
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1994
|
| Series: | Lecture notes in mathematics
1591 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 180 S. |
| ISBN: | 354058465X |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface vii
1. Real Finsler geometry
1.0 Introduction 1
1.1 Non linear connections 3
1.1.1 Preliminaries 3
1.1.2 Horizontal and vertical bundles 5
1.1.3 Local coordinates 11
1.1.4 Geodesies 14
1.2 Vertical connections 15
1.2.1 Definitions 15
1.2.2 Change of coordinates 17
1.2.3 Linear connections on M 18
1.3 Torsion and curvature 19
1.3.1 Connections and differentials on tensor bundles 19
1.3.2 The torsion 21
1.3.3 The curvature 22
1.4 The Cartan connection 24
1.4.1 Finsler metrics 24
1.4.2 The Cartan connection 26
1.4.3 The horizontal flag curvature 30
1.5 First and second variations 32
1.5.1 The setting 32
1.5.2 The first variation of the length integral 36
1.5.3 The second variation of the length integral 38
1.6 Tie exponential map 39
1.6.1 Parallel transport 39
1.6.2 Geodesies 40
1.6.3 The Gauss lemma 45
1.6.4 Geodesies are locally minimizing 46
1.6 Jacobi Gelds and Auslander s theorems 51
1.7.1 Jacobi fields 51
1.7.2 The Morse index form 55
1.7.3 The Cartan Hadamard and Bonnet theorems 59
2. Complex Finsler geometry
2.0 Introduction 63
2.1 Complex non linear connections 64
2.1.1 Preliminaries 64
2.1.2 Change of coordinates 67
2.1.3 Horizontal and vertical bundles 68
2.1.4 Local coordinates 74
vi
2.2 Complex vertical connections 76
2.2.1 Definitions 76
2.2.2 Good vertical connections 77
2.2.3 Connections on complex tensor bundles 79
2.2.4 The torsions 80
2.2.5 The curvature 81
2.3 Tie Chem Finsler connection 84
2.3.1 Complex Finsler metrics 84
2.3.2 The Chern Finsler connection 87
2.3.3 Some computations 89
2.3.4 Torsions and curvatures 92
2.3.5 Kahler Finsler metrics 93
2.4 Variations of the length integral 96
2.4.1 The setting 96
2.4.2 The first variation formula 99
2.4.3 The second variation formula 102
2.5 Holomorphic curvature 105
2.5.1 Symmetry properties of the horizontal curvature 105
2.5.2 The holomorphic curvature 108
2.6 Tie Cartan connection vs. the Chem Finsler connection Ill
2.6.1 The radial vector fields Ill
2.6.2 The horizontal bundles 115
2.6.3 The covariant derivatives 119
2.6.4 The horizontal curvatures 123
3. Manifolds with constant holomorphic curvature
3.0 Introduction 127
3.1 Geodesic complex curves 128
3.1.1 Definitions and properties 128
3.1.2 The existence theorem 133
3.1.3 A characterization of the Kobayashi metric 142
3.2 Manifolds with constant nonpositive holomorphic curvature 147
3.2.1 A complex Cartan Hadamard theorem 147
3.2.2 The Monge Ampere exhaustion 154
3.3 Characterization ofC and of convex circular domains 161
3.3.1 Geometry of the Monge Ampere foliation 161
3.3.2 A characterization of C 166
3.3.3 A characterization of convex circular domains 167
References 171
List of symbols 175
Index 179
|
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| id | DE-604.BV009790286 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:40:55Z |
| institution | BVB |
| isbn | 354058465X |
| language | English |
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| physical | IX, 180 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Abate, Marco 1962- Verfasser (DE-588)102225118X aut Finsler metrics a global approach ; with applications to geometric function theory Marco Abate ; Giorgio Patrizio Berlin [u.a.] Springer 1994 IX, 180 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1591 Finsler-Metrik (DE-588)4359417-7 gnd rswk-swf Finsler-Raum (DE-588)4154449-3 gnd rswk-swf Finsler-Raum (DE-588)4154449-3 s DE-604 Finsler-Metrik (DE-588)4359417-7 s Patrizio, Giorgio Verfasser aut Lecture notes in mathematics 1591 (DE-604)BV000676446 1591 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006477413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abate, Marco 1962- Patrizio, Giorgio Finsler metrics a global approach ; with applications to geometric function theory Lecture notes in mathematics Finsler-Metrik (DE-588)4359417-7 gnd Finsler-Raum (DE-588)4154449-3 gnd |
| subject_GND | (DE-588)4359417-7 (DE-588)4154449-3 |
| title | Finsler metrics a global approach ; with applications to geometric function theory |
| title_auth | Finsler metrics a global approach ; with applications to geometric function theory |
| title_exact_search | Finsler metrics a global approach ; with applications to geometric function theory |
| title_full | Finsler metrics a global approach ; with applications to geometric function theory Marco Abate ; Giorgio Patrizio |
| title_fullStr | Finsler metrics a global approach ; with applications to geometric function theory Marco Abate ; Giorgio Patrizio |
| title_full_unstemmed | Finsler metrics a global approach ; with applications to geometric function theory Marco Abate ; Giorgio Patrizio |
| title_short | Finsler metrics |
| title_sort | finsler metrics a global approach with applications to geometric function theory |
| title_sub | a global approach ; with applications to geometric function theory |
| topic | Finsler-Metrik (DE-588)4359417-7 gnd Finsler-Raum (DE-588)4154449-3 gnd |
| topic_facet | Finsler-Metrik Finsler-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006477413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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